I've coined this term, 'drama of the inexplicable,' to help categorize a certain kind of movie or story, that involves inexplicable happenings and generates tension and atmosphere from withholding any clear explanation. Jeff Nichols' Take Shelter, or Peter Weir's Picnic at Hanging Rock and The Last Wave might be examples, as is Don't Look Now. Perhaps Children of Men fits into this, a little more loosely, for its unexplained epidemic of infertility. HBO's The Leftovers and French series Les Revenants are also examples, in television. Perhaps Jacob's Ladder if you ignore the final title cards. I just watched a movie on Netflix called H. which fits in this category too.
These movies involve weird stuff that doesn't have an easily classifiable supernatural explanation, unlike other movies that are easily labeled: "ghosts and the afterlife" (The Sixth Sense), "telekinesis" (Carrie), "the Devil" (Angel Heart) and so on. Dramas of the inexplicable may thrill, may be horrific, but are not thrillers or horror movies exactly. The inexplicable happenings cause conflict but solving or resolving the conflict is not the point of the story, and not what ultimately happens -- these stories are ultimately more about people than the unexplained stuff, about how they react and cope with things (or can't cope with them).
Any other examples of this y'all can think of?